Why was Claire in the hut? - She was brought there by her daddy, Christian Shephard (so yes, it was him) he appeared to her in episode 10, she left the baby, and followed him.

How the hell are they gonna move the island? - Honestly, I have no idea, it could be something with magnetism but óne thing is certain: they are not gonna push it away.

What was the thing strapped around that guy Martins arm? - Again, no idea, first I thought it was a bomb, but that's unlikely, maybe something to prevent him from getting sick?

How come de dead doctor body turned up at the island before he was killed? - Because of the time difference, it's hard to tell how much exactly because I don't know if the island is moving or not, so it could be a constant difference or not.

I hope I could help!

I will try and answer them.
Claire was in the hut because her dad took her there to keep her safe.
Christian shepard ( Claire's dad )was in the hut.
No idea how they will move the island!
The thing on Martins arm could a weapon of some sorts.
There are time differences between the island and the boat thats why the doctor turned up dead on the island before he was murdered on the boat.

Thanks that really has helped the one thing that is still buggung me is how claire was acting in the hut, she was not acting like a mother who had just abbandoned her baby! She seemed very different like she was hypnotised or somthing! Can't wait till the next episode I wonder how many are left?!

Claire could be drugged or maybe she's dead, who knows?

the doc's dead body makes no sense at all it showed up a couple of episodes back on the beach.this episode they only just slit his throat and threw him in sea.the army guy even told the doc seconds before that they found his body..

also the helicopter set off more or less same time as the doc was thrown in water so why didnt we see helicopter coming earlier obviously travels faster but still doesnt make sense.ahhh actually could just been a body with white jacket on

Maybe the thing on Keamy's arm was functionless - it was just there to scare and distract Gault so he could shoot him.

Could be, altough almost nothing in Lost is functionless, it looked a bit like a bom but he doesn't seem like the type that blows himself up

it could be a remote control for the plastic explosive on the boat that Desmond found.

The thing on keamys arm is a remote so if Keamy dies then the boat blows up!!! And i am guessing that the Doctors dead body did not follow the bearings so landed at a different time whilst the helicopter followed the bearings so landed in real time. Finally i reckon by moving the island it will change the safety bearing so could cause problems.

I agree with Rock_Smurf, the thing on Keamy's arm connects back to the boat. Not sure why, but I'm sure it's part of his big, diabolical plan.

As for Claire, my theory is she's dead, but only reazlized it once Christian told her. That's why she left Aaron and followed him. There are lots of little clues I think have been pointing to that.